Possible to set render border exactly
You can access the render border values via the outliner if you change its display mode to 'Datablocks':



You can then navigate through the tree structure of the outliner to the border values via Scenes> Scene (may be different depending on the name of your actual scene)> Render Data:



The border values can be set from 0-1, so unfortunately you can't set exact pixel coordinates without some maths. 0 is the left side of the camera and 1 is the right side of the camera for the 'x' values (or the bottom and top sides of the camera for the 'y' values).